Optimum stratification for allocation proportional to strata totals for scrambled response

Abstract

The paper considers the problem of finding optimum strata boundaries to optimize the estimation of sensitive/stigmatized characters when sample sizes from different strata are allocated proportionally to strata totals of the auxiliary variable. Assuming the form of the regression of the estimation variable y on the auxiliary variable x as $\mathit{y}=\mathit{\eta }\mathrm{(}\mathit{x}\mathrm{)}+\mathit{e}$ and the form of the conditional variance $\mathit{V}\mathrm{(}\mathit{y}\mid \mathit{x}\mathrm{)}$ , the rule for finding approximate optimum strata boundaries is proposed. The limiting expression of the variance of the estimator of mean in optimum stratification has also been obtained.